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受欢迎的三角函数 >

7tan(x)sin(x)-2sin(x)=0

解答

7 tan (x) sin (x) - 2 sin (x) = 0

解答

x = 2 πn, x = π + 2 πn, x = 0.27829 \dots + πn

+1

度数

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 15.94539 \dots^{\circ} + 18 0^{\circ} n

求解步骤

7 tan (x) sin (x) - 2 sin (x) = 0

分解

7 tan (x) sin (x) - 2 sin (x) : sin (x) (7 tan (x) - 2)

7 tan (x) sin (x) - 2 sin (x)

因式分解出通项

sin (x)

= sin (x) (7 tan (x) - 2)

sin (x) (7 tan (x) - 2) = 0

分别求解每个部分

sin (x) = 0 or 7 tan (x) - 2 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

sin (x) = 0

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

7 tan (x) - 2 = 0 : x = arctan (\frac{2}{7}) + πn

7 tan (x) - 2 = 0

将

2

到右边

7 tan (x) - 2 = 0

两边加上

2

7 tan (x) - 2 + 2 = 0 + 2

化简

7 tan (x) = 2

7 tan (x) = 2

两边除以

7

7 tan (x) = 2

两边除以

7

\frac{7 tan ( x )}{7} = \frac{2}{7}

化简

tan (x) = \frac{2}{7}

tan (x) = \frac{2}{7}

使用反三角函数性质

tan (x) = \frac{2}{7}

tan (x) = \frac{2}{7}

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{2}{7}) + πn

x = arctan (\frac{2}{7}) + πn

合并所有解

x = 2 πn, x = π + 2 πn, x = arctan (\frac{2}{7}) + πn

以小数形式表示解

x = 2 πn, x = π + 2 πn, x = 0.27829 \dots + πn

作图

流行的例子

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